Related papers: Localization and Toeplitz Operators on Polyanalyti…
This paper studies the boundary behavior of the Berezin transform on the C*-algebra generated by the analytic Toeplitz operators on the Bergman space.
In this paper we investigate the reproducing kernel Hilbert space where the polylogarithm appears as kernel functions. This investigation begins with the properties of functions in this space, and here a connection to the classical Hardy…
In a recent article, Dumitru Popa proved an operator version of the Korovkin theorem. We recall the quantitative version of the Korovkin theorem obtained by O. Shisha and B. Mond in 1968. In this paper, we obtain a quantitative estimate for…
In this paper we study the Toeplitz algebra, which is generated by Toeplitz operators with bounded symbols on the Fock space $F^p_{\alpha}$. We show that the Toeplitz algebra coincides with each of the algebras generated by band-dominated,…
For the Weyl-Heisenberg group, convolutions between functions and operators were defined by Werner as a part of a framework called quantum harmonic analysis. We show how recent results by Feichtinger can be used to extend this definition to…
In the Gelfand-Shilov setting, the localisation operator $A^{\varphi_1,\varphi_2}_a$ is equal to the Weyl operator whose symbol is the convolution of $a$ with the Wigner transform of the windows $\varphi_2$ and $\varphi_1$. We employ this…
We study concentration operators acting on the Fourier symmetric Sobolev space $H$ consisting of functions $f$ such that $\int_{\mathbb{R}} |f(x)|^2(1+x^2) dx + \int_{\mathbb{R}} |\hat{f}(\xi)|^2(1+\xi^2) d\xi < \infty $. We find that the…
We discuss the range spaces of Toeplitz operators with co-analytic symbols where we focus on the boundary behavior of the functions in these spaces as well as a natural orthogonal decomposition of this range.
In this paper, we discuss index theory for Toeplitz operators on a discrete quarter-plane of two-variable rational matrix function symbols. By using Gohberg-Krein theory for matrix factorizations, we extend the symbols defined originally on…
Let $X$ be a space of homogeneous type and $L$ be a nonnegative self-adjoint operator on $L^2(X)$ satisfying Gaussian upper bounds on its heat kernels. In this paper we develop the theory of weighted Besov spaces…
We demonstrate that the weight operator associated with a submultiplicative filtration on the section ring of a polarized complex projective manifold is a Toeplitz operator. We further analyze the asymptotics of the associated weighted…
The asymptotic results for Berezin-Toeplitz operators yield a strict quantization for the algebra of smooth functions on a given Hodge manifold. It seems natural to generalize this picture for quantizable pseudo-K\"ahler manifolds in…
We study Toeplitz operators on the Bargmann space, with Toeplitz symbols that are exponentials of complex quadratic forms, from the point of view of Fourier integral operators in the complex domain. Sufficient conditions are established for…
One of the major questions in the theory of Toeplitz operators on the Bergman space over the unit disk $\mathbb D$ in the complex plane $\mathbb C$ is a complete description of the commutant of a given Toeplitz operator, that is the set of…
We consider separately radial (with corresponding group $\mathbb{T}^n$) and radial (with corresponding group $\mathrm{U}(n))$ symbols on the projective space $\mathbb{P}^n(\mathbb{C})$, as well as the associated Toeplitz operators on the…
The purpose of this paper is to systematically study compactness and essential norm properties of operators on a very general class of weighted Fock spaces over $\C$. In particular, we obtain rather strong necessary and sufficient…
Quantum harmonic analysis on phase space is shown to be linked with localization operators. The convolution between operators and the convolution between a function and an operator provide a conceptual framework for the theory of…
We obtain a noncommutative multivariable analogue of Louhichi and Olofsson characterization of Toeplitz operators with harmonic symbols on the weighted Bergman space $A_m({\bf D})$, as well as Eschmeier and Langendorfer extension to the…
Extensions of coorbit spaces for functions to operators have been introduced by two different groups in \cite{doelumcskr24} and \cite{k\"obaLOC25}, where one is based on the coorbit theory of Feichtinger-Gr\"ochening while the other is…
In their previous work, the authors proved the Berger-Coburn phenomenon for compact and Schatten $S_p$ class Hankel operators $H_f$ on generalized Fock spaces when $1<p<\infty$, that is, for a bounded symbol $f$, if $H_f$ is a compact or…